User talk:Zhenlige: Difference between revisions

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:: It's totally fair that you're not familiar with very large EDOs or very complex intervals if for no other reason than there just being way too many of both to cover. That said, what's interesting about schismatic is that it has implications for more subgroups than just the 5-limit- rather, it also has significant implications for other subgroups involving the 5-limit. I'm curious, how familiar are you with certain 11-limit intervals like 11/8, 16/11, 11/10, 33/32, and, of course, 243/242? Although I'm not convinced that you're at all familiar with the last of those five, I ask because I nevertheless want to see how familiar you are with some of these intervals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:29, 10 June 2025 (UTC)

::: I usually think 11-limit intervals as “neutral intervals ± fractions of rastma (243/242)”, just like how NFJS represents them. (I am not satisfied with the RoT's of FJS and NFJS, though.) For example, 11/8 is sA4 − 1/2 rastma, 33/32 is sA1 − 1/2 rastma, and so on. For intervals involving both 11 and 5 or both 11 and 7, that makes less sense, because thinking 11/10 as “n2<sub>5</sub> − 1/2 rastma” does not clearly show its properties since “n2<sub>5</sub>” is already a strange interval. For specific intervals there may be other viewpoints, e.g. 11/10 as “something between 10/9 and 12/11” or “near 1/3 of the interval 4/3”. Actually I rarely think such intervals independently, but rather as part of a larger structure. 13-limit intervals are very novel to me — actually I am even more familiar with 17 and 19 due to my early research on near-12edo intervals. --[[User:Zhenlige|Zhenlige]] ([[User talk:Zhenlige|talk]]) 02:35, 11 June 2025 (UTC)

:::: Funny you should mention not being satisfied with the terms of the FJS and NFJS. The nomenclature that goes with [[Alpharabian tuning]] is actually more precise. For instance, 33/32 is an ultraprime while 11/8 is a paramajor fourth. In contrast, 729/704 is an infra-augmented prime, while 243/176 is an infra-augmented fourth- you might want to look up these more complicated 2.3.11 intervals if you're not already familiar with them. I should mention that in addition to 11/10, a type of submajor second, being roughly one third of 4/3, it actually differs from an ultra-augmented prime (think an apotome plus 33/32) by a schisma. This naturally means that in schismatic temperaments, these two intervals are enharmonic. Any thoughts on all this? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:46, 11 June 2025 (UTC)

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 :: It's totally fair that you're not familiar with very large EDOs or very complex intervals if for no other reason than there just being way too many of both to cover.  That said, what's interesting about schismatic is that it has implications for more subgroups than just the 5-limit- rather, it also has significant implications for other subgroups involving the 5-limit.  I'm curious, how familiar are you with certain 11-limit intervals like 11/8, 16/11, 11/10, 33/32, and, of course, 243/242?  Although I'm not convinced that you're at all familiar with the last of those five, I ask because I nevertheless want to see how familiar you are with some of these intervals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:29, 10 June 2025 (UTC)
+::: I usually think 11-limit intervals as “neutral intervals ± fractions of rastma (243/242)”, just like how NFJS represents them. (I am not satisfied with the RoT's of FJS and NFJS, though.) For example, 11/8 is sA4 − 1/2 rastma, 33/32 is sA1 − 1/2 rastma, and so on. For intervals involving both 11 and 5 or both 11 and 7, that makes less sense, because thinking 11/10 as “n2<sub>5</sub> − 1/2 rastma” does not clearly show its properties since “n2<sub>5</sub>” is already a strange interval. For specific intervals there may be other viewpoints, e.g. 11/10 as “something between 10/9 and 12/11” or “near 1/3 of the interval 4/3”. Actually I rarely think such intervals independently, but rather as part of a larger structure. 13-limit intervals are very novel to me — actually I am even more familiar with 17 and 19 due to my early research on near-12edo intervals. --[[User:Zhenlige|Zhenlige]] ([[User talk:Zhenlige|talk]]) 02:35, 11 June 2025 (UTC)
+:::: Funny you should mention not being satisfied with the terms of the FJS and NFJS.  The nomenclature that goes with [[Alpharabian tuning]] is actually more precise.  For instance, 33/32 is an ultraprime while 11/8 is a paramajor fourth.  In contrast, 729/704 is an infra-augmented prime, while 243/176 is an infra-augmented fourth- you might want to look up these more complicated 2.3.11 intervals if you're not already familiar with them.  I should mention that in addition to 11/10, a type of submajor second, being roughly one third of 4/3, it actually differs from an ultra-augmented prime (think an apotome plus 33/32) by a schisma.  This naturally means that in schismatic temperaments, these two intervals are enharmonic.  Any thoughts on all this? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:46, 11 June 2025 (UTC)